Phase transitions in simplified models with long-range interactions

Abstract

We study the origin of phase transitions in some simplified models with long range interactions. For the ring model, we show that a possible new phase transition predicted in a recent paper by Nardini and Casetti from an energy landscape analysis does not occur. Instead of such phase transitions we observe a sharp, although without any non-analiticity, change from a core-halo to an only core configuration in the spatial distribution functions for low energies. By introducing a new class of solvable simplified models without any critical points in the potential energy, we show that a similar behaviour to the ring model is obtained, with a first order phase transition from an almost homogeneous high energy phase to a clustered phase, and the same core-halo to core configuration transition at lower energies. We discuss the origin of these features of the simplified models, and show that the first order phase transition comes from the maximization of the entropy of the system as a function of energy an an order parameter, as previously discussed by Kastner, which seems to be the main mechanism causing phase transitions in long-range interacting systems.

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Cited by in corpus (5)

• Local thermodynamics and the generalized Gibbs-Duhem equation in systems with long-range interactions
• Heat conduction in chains of non-locally coupled harmonic oscillators: mean-field limit
• Geometry of the energy landscape of the self-gravitating ring
• Ensemble Inequivalence and Maxwell Construction in the Self-Gravitating Ring Model
• Brownian regime of finite-N corrections to particle motion in the XY hamiltonian mean field model